Investigating the Nonlinear Stiffness of Granular Materials: A DEM Perspective on Stress Path Dependence

Abstract

While the effect of stress path on the nonlinear behavior of granular materials has long been recognized, its influence on stiffness degradation remains not fully understood and has not been systematically explored using the discrete element method (DEM) at the microscale. This study employs DEM to simulate triaxial tests and investigate the underlying mechanisms of stress path‐dependent nonlinear stiffness. The evolutions of microscopic parameters, including mechanical coordination number (MCN), contact slippage ratio (Rs), and anisotropies of contact normal and contact forces, were monitored. The results show that stress path significantly influences shear stiffness. At very small strain, shear stiffness is consistent across different stress paths under initial isotropic stress states but diversifies under anisotropic conditions. At small‐to‐medium strain, stiffness degradation rates vary with stress path and are further affected by initial stress condition and relative density. For isotropic stress states, paths associated with higher average normal contact force exhibit larger shear stiffness, lower Rs and higher MCN. By contrast, under anisotropic stress states, unloading paths demonstrate higher stiffness than loading paths, with a rapid decrease of Rs due to reverse particle motions. The influence of on stiffness diminishes in anisotropic conditions, making Rs and MCN the dominant factors, where higher MCN and lower Rs correspond to greater stiffness. A reference shear strain characterizing contact slippage is introduced, based on which several quantitative relationships are proposed to link contact slippage with stiffness degradation.